Problem: Which of the following numbers is a factor of 85? ${5,6,7,8,14}$
By definition, a factor of a number will divide evenly into that number. We can start by dividing $85$ by each of our answer choices. $85 \div 5 = 17$ $85 \div 6 = 14\text{ R }1$ $85 \div 7 = 12\text{ R }1$ $85 \div 8 = 10\text{ R }5$ $85 \div 14 = 6\text{ R }1$ The only answer choice that divides into $85$ with no remainder is $5$ $ 17$ $5$ $85$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $5$ are contained within the prime factors of $85$ $85 = 5\times17 5 = 5$ Therefore the only factor of $85$ out of our choices is $5$. We can say that $85$ is divisible by $5$.